Mass of a solid

Right now I'm learning about the Change of Variables formula and applications of integration, and I'm having trouble with this question:

Find the mass of the solid bounded by the cylinder x^2+y^2=2x and the cone z^2=x^2+y^2 if the density is delta=sqrt(x^2+y^2).

I have the idea that I should switch to cylindrical coordinates. So I would let x=rcostheta, y=rsintheta, and z=z. I get that delta=r, but I am having trouble figuring out what my limits of integration will be. Any help would be appreciated.

Yes, I agree that, because of the circular symmetry, cylindrical coordinates should simplify the integration. I assume that by "the solid bounded by" the cylinder and cone, they mean the region between the two "nappes" of the cone, inside the cylinder.

The easy part- will range from to . Slightly harder: Since the cone, in cylindrical coordinates, is and the cylinder by ( and : and we can cancel an "r"), the cone and cylinder intersect when . For each [itex]\theta[/itex], z ranges from to . Finally, for each z and , r ranges from the cone out to the cylinder. The cone is r= |z| (r is positive, of course) and the cylinder as before.